Making her Walt Disney Concert Hall debut, Natalie Cole may have started 20 minutes late but she made up for it with a greater-than-the-usual-90-minute set of American songbook treasures, holiday tunes and early career hits. The sensational woman of song, who is the first performer of the Hall’s 2011 jazz season, proudly strutted out to the stage in a glistening silvery gown-and 7-inch heels-and showed off just how far she’s come since recovering from Hepatits C.

It was in the winter of 2008 that she was diagnosed with the disease during a routine examination, which she admitted in her autobiography, “Angel On My Shoulder,” was likely the result of her drug use decades ago. And in one of her first public appearances on a big stage after her near-death experience, Cole made a surprise appearance at last year’s LaBelle reunion at the Nokia Theatre, when she appeared gaunt.

But here she was, back in full form-and with a lot to sing. She said she was going to sing the best songs of the standards. And that’s where she started. With her longtime, Black female conductor Gail Deadrick (such a wonderful visual!), and accompanied by a jazz sextet, two background singers and a 13-piece brass ensemble, Cole and company swung through Harold Arlen-Johnny Mercer’s “Come Rain or Come Shine” and Al Jolson’s “I Found My Love in Avalon,” which was also recorded by father Nat King Cole.

She was fortunate, she said, “to have grown up around a man some called ‘Ol’ Blue Eyes’ and ‘the chairman of the board'” but whom she called ‘Uncle Frank,’ after which she launched into a slower, more swinging version of the chairman’s “Nice and Easy Does It,” penned by Alan and Marilyn Bergman.

Moving beyond the songs of her father and Uncle Frank’s generation, she chose the vibrant, three-quarter-time “Better Than” off her 2002 CD, “Ask a Woman Who Knows”; and, with Deadrick tending piano, did a smooth bossa nova beat on Michael Franks’ “Tell Me All About It.” On Antonio Carlos Jobim’s “Somewhere In the Hills,” she glided over, under and around the Brazilian notes and beats, while Lambert Hendricks and Ross’ “Fiesta in Blue” and Jack Jones’ “Roses and Lollipops” became slow, jazzy grooves in her renditions. Cole’s inimitable style does not strain for any notes; she hits every single note with ease, never overpowering the music, letting it speak for itself.

A bit of history lesson followed, with Cole explaining that “Smile,” originally sung by Nat King Cole, had been given to him by the song’s composer, Charlie Chaplin; she herself covered it on her 1991 album “Unforgettable . . . With Love.”

And then, right on cue, she segued into that CD’s title track and, with home videos of Nat, Natalie, mom and sister projected on the Hall’s huge screen and accompanied by her father’s/the original sax soloist Pete Christlieb. Cole sang “Unforgettable.”

The set could have ended there but no, she still had to do abbreviated versions of two of her biggest pop hits-“Mr. Melody” and “This Will Be”-as well as a few Christmas tunes, including the joyous “Caroling, Caroling” from a concert she performed at last year with the Mormon Tabernacle Choir’s annual Christmas concert, “The Wondrous Gift of Christmas.”

A warm and overwhelmingly appreciative audience brought her back for an encore of, what else? “The Christmas Song” (‘Chestnuts roasting on an open fire . . .’).

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